Granular micromechanics model for cementitious materials

Granular micromechanics is a strong tool for modeling the behavior of different types of materials wherein the global (i.e., macroscopic) response of the material is assumed to be derivable as a summation of the local (i.e., microscopic) responses between grains that compose the material point. Cementitious materials are clear examples of micromechanically complicated materials in which microscopic response significantly influences the global behavior. Modeling of these materials using traditional tensorial constitutive equations leads to the neglect of several microscopic features. Because in granular micromechanics, interactions between all particles are taken into account separately, the method naturally provides a robust tool for implementing different micromechanical features in the material structure. By introducing potential and dissipation functions at the local scale, a Clausius–Duhem type inequality in the microscopic scale is obtained and an expression of macroscopic Cauchy stress in terms of interparticle kinematics and forces is developed. Subsequently, we introduce a set of interparticle interaction functions to establish thermodynamically consistent intergranular constitutive relations particularly applicable to cementitious materials. As a result we obtain force laws which ensure asymmetric behavior in tension and compression. Updated loading–unloading–reloading criteria are implemented in the model with the capability of modeling damage and plasticity. Damage parameter in tangential direction is defined as a function of not only the tangential displacement component, but also the normal component of displacement as well as the average stress. Normal compressive force law parameters are also obtained as functions of the average stress which enables the model to capture the effects of confining stress. Tensile and compressive triaxial tests with different confining stresses have been simulated indicating “brittle” to “ductile” transition of the material behavior by increasing the confining stress. Biaxial failure surface is computed and the effect of change in the direction of loading and the resulting induced anisotropy on the failure stress state is captured. Moreover, volume control tests with different ratios of normal versus lateral strain increments and with different initial hydrostatic confining pressures have been modeled providing failure envelopes in the q–p (deviatoric stress–mean stress) plane

Continuum Modeling Using Granular Micromechanics Approach: Method Development and Applications

This work presents a constitutive modeling approach for the behavior of granular materials. In the granular micromechanics approach presented here, the material point is assumed to be composed of grains interacting with their neighbors through different inter-granular mechanisms that represent material’s macroscopic behavior. The present work focuses on (i) developing the method for modeling more complicated material systems as well as more complicated loading scenarios and (ii) applications of the method for modeling various granular materials and granular assemblies. A damage-plasticity model for modeling cementitious and rock-like materials is developed, calibrated, and verified in a thermo-mechanically consistent manner. Grain-pair interactions in normal tension, normal compression, and tangential directions have been defined in a manner that is consistent with the material’s macroscopic behavior. The resulting model is able to predict, among other interesting issues, the effects of loading induced anisotropy. Material’s response to loading will depend on the loading history of grain-pair interactions in different directions. Thus the model predicts load-path dependent failure. Due to the inadequacies of first gradient continuum theories in predicting phenomena such as shear band width, wave dispersion, and frequency band-gap, the presented method is enhanced by incorporation of non-classical terms in the kinematic analysis. A complete micromorphic theory is presented by incorporating additional terms such as fluctuations, second gradient terms, and spin fields. Relative deformation of grain-pairs is calculated based on the enhanced kinematic analysis. The resulting theory incorporates the deformation and forces in grain-pair interactions due to different kinematic measures into the macroscopic behavior. As a result, non-classical phenomena such as wave dispersion and frequency band-gaps can be predicted. Using the grain-scale analysis, a practical approach for calibrating model parameters corresponding to micromorphic continua is also presented that can be used for any given material system or grain assembly

Thermomechanics-based granular micromechanics rate dependent coupled damage-plasticity model

Materials with granular or pseudogranular microstructure exhibit significant effect of grain-scale mechanisms on the macroscale behavior. In these material systems, the relevant representative unit can be described as collection of grains formed by the aggregations of atoms or molecules such that the intragranular interactions are qualitatively different from intergranular interactions. In some materials, such grains are easily identifiable with distinct grain boundaries, such as in the cases of grain packings. However, there are a number of materials in which the grain identification is not straightforward although they exhibit a strongly granular texture. In either case, the evidence of granular nature of materials and the ideas of coarse graining by combining atoms and molecules into larger grains have been prevalent. The granular micromechanics paradigm offers a feasible approach for developing continuum models for these materials. The granular micromechanics approach traces its genesis to the continuum models of grain packings developed in the second-half of the last century; however, this approach has antecedents in the early development of continuum mechanics. The resultant models offer the versatility of investigating the influence of both the macro-scale parameters and the grain-scale parameters on the overall stress–strain response by incorporating the effect of nearest neighbor grain interactions through the intergranular force–displacement relationship and orientation vector. The advantages are clear because (i) the computational needs are far smaller than that of other particulate approaches, such as DEM; (ii) the models naturally exhibit macro-scale effects such as material density and inherent and loading-induced anisotropy effects; and (iii) can readily represent microscale effects of particle interactions, including rate effects. In recent years, these models have undergone further refinement and have been successfully applied to model a number of phenomena exhibited by granular materials. In the proposed presentation, we will trace the development of granular micromechanics framework and focus on some recent results obtained by derivations based upon thermomechanics, which allow for the evaluation of thermodynamic consistency of the derived models

Discrete element modeling of strongly deformed particles in dense shear flows

The discrete element method (DEM) proposed by Cundall and Strack [1] is a widely used numerical approach to study the fundamentals of particulate matter at the particle scale. In our present study, the flow behavior of dense configurations of soft particles was studied by means of a new formulation of the multi-contact force closure for the DEM. The first step was to verify the response of the new force closure, and calibrate its parameters based on a comparison of the results for simple uniaxial compression with results from a reference simulation. This reference simulation used a highly accurate nonlocal formulation of contact mechanics in the quasi-static limit [2], which accounts for the interplay of deformations due to multiple contact forces acting on a single particle. The newly developed and calibrated model results show significant improvement over those derived via the existing multi-contact model. Also, the dependence of the stress in the sheared granular matter on the Poisson's ratio was unveiled when using the newly derived advanced multi-contact force closure. Therefore, an extensive campaign of simple shear flow simulations was performed (at a fixed volume of the simulation box) to probe the effect of particle volume fraction and the speed of shearing. These simulations show that the stress at particle volume fractions larger than a critical value depends not only on the friction coefficient and particle stiffness, but also on the Poisson's ratio of the material. Finally, we report a response surface for the pressure in a sheared particle bed as a function of all key influence parameters. This response surface is beneficial for calibrating DEM model parameters in extremely dense flow configurations.</p

Granular micromechanics modeling of beams, plates, and shells

We present constitutive laws of structural members, such as beams, plates and shells, using the granular micromechanics approach. These relationships between internal resultants (i.e., internal forces and moments) and kinematic variables (i.e., strains and curvatures) depend solely on the microstructural properties of the constituents and the structure geometry. The macroscopic behavior is derived by investigating the average behavior of grain-pair interactions in all generic directions and, thus, automatically represent complex loading-induced and path-dependent anisotropic responses. We specifically derive closed-form solutions for the constitutive relationship of structural members made of both uniform and functionally graded materials, as functions of grain-scale parameters. Furthermore, we demonstrate the versatility and computational efficiency of the proposed approach, as well as its applicability to nonlinear material systems not amenable to closed-form solutions, by studying structural members made of particle–binder composites that exhibit failure-to-damage deformation mechanisms. These analytical and numerical solutions reveal interesting one-way and two-way coupling behavior between internal forces and moments

Grain-Size Effects on Mechanical Behavior and Failure of Dense Cohesive Granular Materials †

The grain sizes can significantly influence the granular mechano-morphology, and consequently, the macro-scale mechanical response. From a purely geometric viewpoint, changing grain size will affect the volumetric number density of grain-pair interactions as well as the neighborhood geometry. In addition, changing grain size can influence initial stiffness and damage behavior of grain-pair interactions. The granular micromechanics approach (GMA), which provides a paradigm for bridging the grain-scale to continuum models, has the capability of describing the grain size influence in terms of both geometric effects and grain-pair deformation/dissipation effects. Here the GMA based Cauchy-type continuum model is enhanced using simple power laws to simulate the effect of grain size upon the volumetric number density of grain-pair interactions, and the parameters governing grain-pair deformation and dissipation mechanisms. The enhanced model is applied to predict the macroscopic response of cohesive granular solids under conventional triaxial tests. The results show that decreasing grain-sizes can trigger brittle-to-ductile transition in failure. Grain size is found to affect the compression/dilatation behavior as well as the post-peak softening/hardening of granular materials. The macro-scale failure/yield stress is also found to have an inverse relationship with grain-sizes in consonance with what has been reported in the literature

Discrete element modeling of strongly deformed particles in dense shear flows

The discrete element method (DEM) proposed by Cundall and Strack [1] is a widely used numerical approach to study the fundamentals of particulate matter at the particle scale. In our present study, the flow behavior of dense configurations of soft particles was studied by means of a new formulation of the multi-contact force closure for the DEM. The first step was to verify the response of the new force closure, and calibrate its parameters based on a comparison of the results for simple uniaxial compression with results from a reference simulation. This reference simulation used a highly accurate nonlocal formulation of contact mechanics in the quasi-static limit [2], which accounts for the interplay of deformations due to multiple contact forces acting on a single particle. The newly developed and calibrated model results show significant improvement over those derived via the existing multi-contact model. Also, the dependence of the stress in the sheared granular matter on the Poisson's ratio was unveiled when using the newly derived advanced multi-contact force closure. Therefore, an extensive campaign of simple shear flow simulations was performed (at a fixed volume of the simulation box) to probe the effect of particle volume fraction and the speed of shearing. These simulations show that the stress at particle volume fractions larger than a critical value depends not only on the friction coefficient and particle stiffness, but also on the Poisson's ratio of the material. Finally, we report a response surface for the pressure in a sheared particle bed as a function of all key influence parameters. This response surface is beneficial for calibrating DEM model parameters in extremely dense flow configurations